You'll have to use Server Side Filters to have Record Level Access control.
When creating your database schema, create one field with type user_id. This will be used to identify the owner of that record.
In the user's role define an Advanced Filter to filter only the records owned by the user requesting the data.
Take a look at https://github.com/dreamfactorysoftware/dsp-core/wiki/Server-Side-Filters